EXISTENCE OF SOLUTIONS IN THE α-NORM FOR NEUTRAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

DOI QR Code

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.

R. Benkhalti and K. Ezzinbi, Existence and stability in the ${\alpha}$-norm for some partial functional differential equations with infinite delay, Differential and Integral Equ. 19 (2006), 545-572.
H. Bouzahir, Partial Neutral Functional Differential Equations with Infinite Delay, VDM Verlag Dr. Muller, Saarbrucken, 2010.
L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505. https://doi.org/10.1016/0022-247X(91)90164-U
K. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000.
K. Ezzinbi, X. Fu, and K. Hilal, Existence and regularity in the ${\alpha}$-norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Anal. 67 (2007), 1613-1622. https://doi.org/10.1016/j.na.2006.08.003
X. Fu, On solutions of neutral nonlocal evolution equations with nondense domain, J. Math. Anal. Appl. 299 (2004), 392-410. https://doi.org/10.1016/j.jmaa.2004.02.062
X. Fu, Y. Gao, and Y. Zhang, Existence of solutions for neutral integrodifferential equations with nonlocal conditions, Taiwanese J. Math. 16 (2012), 1879-1909. https://doi.org/10.11650/twjm/1500406803
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.

EXITSENCE OF MILD SOLUTIONS FOR SEMILINEAR MIXED VOLTERRA-FREDHOLM FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCALS vol.28, pp.3, 2015, https://doi.org/10.14403/jcms.2015.28.3.365